1. Radar Polarimetric Retrievals. Anthony Illingworth University of Reading, UK

2. RADAR REFLECTIVITY, Z FOR RAIN Z =  N D 6 (mm 6 m -3 ) SIXTH MOMENT: dBZ = 10log(Z) RAINRATE: R =  N D 3.67 3.67 TH MOMENT EMPIRICALLY Z = aR b “Z= 200 R 1.6 ” ERROR ‘FACTOR OF TWO’ Z has no information on hydrometeor characteristics

3. WHAT IF TARGET IS ICE? Z =  (K ice /K water ) 2 N D 6 (K water ) 2 = 0.93 and K ice =  (ice) 0.205 So K of fluffy snow is very low, now, mass =  * volume so for dry ice Z prop to  mass 2 If ice is wet: K 2 =0.93 so Z much higher: So melting snow: high Z – bright band. HAIL – D large – Z = 60dBZ So Z= 200 R 1.6 Gives R=200mm/hr

4. WHAT CAN POLARISATION ADD? TRANSMIT AND RECEIVE HORIZONTALLY AND VERTICALLY POLARISED WAVE. FOUR NEW PARAMETERS. Consider at low elevation 1. DIFFERENTIAL REFLECTIVITY: ZDR MEASURE REFLECTIVITY WITH HORIZONTAL (ZH) AND VERTICAL (ZV) POLARISATION ZDR = 10 LOG(ZH/ZV)

5. ZDR MESURES MEAN PARTICLE SHAPE – e.g. RAIN. 1mm 3mm 5mm ZH > ZV ZDR = 2dB ZH >>ZV ZDR = 4 dB RAIN: ZDR IS A MEASURE OF MEAN DROP SHAPE/SIZE HAIL: TUMBLES SO ZDR=0dB SNOW/AGGREGATES: look spherical to radar, ZDR=0dB. ZH =ZV ZDR = 10LOG(ZH/ZV)=0dB

6. 2. DIFFERENTIAL PHASE SHIFT, KDP OBLATE HYDROMETEORS (E.G LARGE RAINDROPS) DELAY H WAVE MORE THAN V WAVE. PHASE DIFFERENCE,  DP, INCREASES WITH RANGE KDP is grad of  dp in deg/km RAIN – KDP   R: HAIL NO KDP AGGREGATES – NO KDP PRISTINE XLS – SOME KDP

7. ZDR AND KDP IN RAIN Z >40dBZ In heavy rain ZDR>2dB In heavy rain Phase shift 40degs thru heavy rain

8. 3. LINEAR DEPOLARISATION RATIO, LDR Transmit H, receive H (copolar) and V (x-polar) LDR = 10 log(x-polar/copolar) X-polar return only from oblate particles falling an angle to H or V Highest return for high K – if particles are wet Wet snowflakes LDR = -12dB Dry Pristine Crystals -24dB Dry snow flakes and rain LDR < - 30dB

9. 4. Copolar correlation,  (hv) the correlation between time series of ZH and ZV If particles all the same shape  = 1 Variety of shapes, variety of ratio ah/av then  < 1 Rain:  >0.98 bright band:  approx 0.9 Ground clutter and anaprop (Mie scatter):  = 0. t=1 T=2

10. POLARISATION PARAMETERS FROM CLOUDS LIQUID DROPLETS <1mm SPHERICAL – NO SIGNAL LOW DENSITY AGGREGATES – LOOK SPHERICAL TO THE RADAR – NO SIGNAL FROM MOST ICE CLOUDS. PRISTINE CRYSTALS – viewed at low elevation can have high ZDR and some kdp when viewed at low elevation. If aggregates present then ZDR=0dB, but kdp unaffected Can’t use kdp to estimate iwc because iwc dominated by aggregates. Special case of crystals aligned in electric field in thunderstorm: Where field vertical - negative kdp. Where field at 45 degs – get ldr Can ‘map’ out field – see our web site.

11. POLARISATION PARAMETERS FROM CLOUDS PRISTINE CRYSTALS – viewed at zenith NO ZDR OF KDP (except when alignment in electric field) THEY CAN GIVE LDR OF ABOUT –24dB But X-POLAR RETURN USUALLY BELOW DETECTION LIMIT AT ZENITH IDENTIFY MELTING LAYER LDR= -13dB IN PRECIPTATING CLOUDS CAN IDENTIFY GRAUPEL FROM SNOW BY DIFFERENT LDR WHEN THEY MELT.

12. WHAT USE IS RADAR FOR LWC AND IWC? 1. DIFFERENTIAL ATTENUATION BETWEEN 94 AND 35GhZ RADAR IN LIQUID CLOUDS IS ABOUT 8dB/km/g/m 3 BUT NEED LONGISH DWELLS TO GET PROFILES OF LWC 2. ICE PARTICLE SIZE: 94GHz Mie SCATTERS ONCE D>0.3mm; 35GHz RAYLEIGH SCATTERS SO DUAL WAVELENGTH REFLECTIVITY RATIO GIVES Do IF Do > 0.3mm ONCE YOU KNOW Do, THEN Z AT 35GHz GIVES YOU N DERIVE IWC – ERROR DEPENDS ON ICE DENSITY f(D) GET THIS FROM DUAL DOPPLER VELOCITY DIFFERENCE

13. CLOUDNET: Two years of 24h/7d radar/lidar observations Cabauw, Palaiseau, Chilbolton Categorisation of echoes – ice, liquid, scooled etc. Derive cloud fraction, iwc, lwc, etc. + ERRORS Model data from ECMWF, MeteoFrance, Met Office, RACMO – over the three stations for two years. For real time cloud profiles visit: www.met.reading.ac.uk/radar/realtime And for CloudNET “ /radar/cloudnet/

14. Cloud fraction: 10 day comparison with ECMWF model Initial comparison suggests that clouds are very well represented by the ECMWF model Remember that for 20 m/s wind, one day of data is equivalent to 1700 km of cloud, so very large scale features are being compared here!

15. Cloud fraction:12 Months of Chilbolton data Too much cloud high levels, too little mid-levels –However, frequency of occurrence is better: suggests humidity structure is good, but amount when present is not so good –Low-level clouds are very different in the two models

16. Ice water content (from Z) results Underestimate of mean mid-level IWC in both models –Seems to be due to factor-of-2 error in mean cloud fraction –Mean in-cloud IWC appears to be reasonably good above 4 km (g m -3 )

17. BEST APPLICATION OF POLARISATION IS FOR BETTER RAINRATES. ZDR GIVES YOU MEAN DROP SIZE + Z GIVES YOU N: BETTER ESTIMATE OF RAIN SIZE SPECTRA – BETTER R KDP – PHASE SHIFT – MEASURABLE IN HEAVY RAIN a) R = f(KDP) GIVES R WHEN HAIL PRESENT. b) PHASE SHIFT PROPORTIONAL TO Z ATTENUATION SO METEO FRANCE AND MET OFFICE WILL INSTALL AN OPERATIONAL POLARISATION RADAR IN 2004

18. R from Z alone: major problem is Vertical profile of reflectivity - melting snow :bright band - rapid fall of Z in the ice - near the ground beam in the rain OPERATIONAL RADAR – BEAM 1DEG – 2km WIDE AT 100km RANGE. 30dBZ 0dBZ

19. SUMMARY OF PROBLEMS (AND SOLUTIONS) OF DERIVING R FROM Z ALONE VERTICAL PROFILE OF REFLECTIVITY - USE LDR TO IDENTIFY THE B BAND? ATTENUATION AT C-BAND – USE DIFF PHASE ANAPROP AND CLUTTER USE  ABSOLUTE CALIBRATION OF Z - USE REDUNDANCY OF ZDR AND KDP IN HEAVY RAIN TO CALIB TO 0.5dB. BETTER RAINDROP SPECTRA - USE ZDR.

20. FOR ZDR AND KDP DROP SHAPE MODEL CRUCIAL USE ANDSAGER/GODDARD SHAPES

21. FOR BETTER RAINRATES NEED ZDR ACCURATE TO better than 0.2dB Curves are value of Z for R=1mm/hr for a given ZDR. If observed Z is xdB Higher then R is xdB Above 1mm/hr

22. KDP ONLY USEFUL FOR HEAVY RAIN e.g. 1deg/km is about 40mm/hr. difficult to measure lower values of KDP

23. Z CALIBRATION TECHNIQUE: In rain Z, ZDR and KDP are not independent KDP/Z is a unique function of ZDR: SO along a ray at each gate from observed Z and ZDR calculate theoretical KDP, find theoretical  dp per gate. Adjust Z so computed phase shift agrees with observed phase shift Correct shapes

24. ZDR AND KDP IN RAIN Z >40dBZ In heavy rain ZDR>2dB In heavy rain Phase shift 40degs thru heavy rain

25. CALIBRATION EXAMPLE Observed phase shift along ray is 25 degs. Adjust Z, so that phase shift calculated from observed Z and ZDR agrees with observed phase shift.

26. Polarisation Rainfall Technique R from Z and Z dr Need ZDR to 0.1dB at 3mm/hr for R accurate to 25% Operationally ZDR too noisy for accurate gate by gate R. Noise due to sidelobe mismatch, triple scattering etc. SUGGEST Use domain average so noise in ZDR averages to zero. Calculate best Z-R domain relation from Z and ZDR. Rainfall accuracy of 25% possible for R = 3mm/hr See chapter 5 in Peter Meischner’s (Ed.) forthcoming book: Weather Radar: Advanced Applications – Springer.

27. Polarisation Rainfall Technique R from Z and Z dr Need ZDR to 0.1dB at 3mm/hr for R accurate to 25% Operationally ZDR too noisy for accurate gate by gate R. Noise due to sidelobe mismatch, triple scattering etc. Use domain average so noise in ZDR averages to zero. Calculate best Z-R domain relation from Z and ZDR. Rainfall accuracy of 25% possible for R = 3mm/hr Diff phase shifts only good for heavy rain. Rain of < 30mm/hr caused the flooding of central Europe Use Diff phase shift in heavy rain to calibrate Z to 0.5dB.

28. Drop Spectra: Normalised Gamma Function We assume that the drop spectra can be represented by the normalised gamma distribution D o = Median volume drop size The average size of the drops N w = Normalised drop concentration Normalised for constant liquid water content with changes in  The number of drops  = width of spectrum High values correspond to a narrow drop spectrum – most drops about the same size. Where: Drop size (mm) 10 4 10 3 10 2 10 1 10 0 10 -1 0 0.5 1 1.5 2 2.5 Number of drops / m 3 / mm D o = 1 mm, N w = 8000 m -3 mm -1

29. Z-R if N w constant We will now presume  = 5 N w and D o can vary Now suppose that as rain gets heavier, N w remains constant, but D o increases. The ‘ZPHI’ method of Testud et al (2000) assumes N w is constant and derives it and hence a from the integrating along the ray, using Z and the total differential phase shift. Drop size (mm) 10 3 10 2 10 1 10 0 0 1 2 3 4 5 6 7 N w = 8000 m -3 mm -1  = 5 Number of drops / m 3 / mm

30. Heavier rain D o Increases: N w  D o -1 If: N w  D o -1 As drops get bigger, there are less of them. This is the UK default Stratiform rain. R 1.6 More ice aggregation Larger but fewer snowflakes 10 4 10 3 10 2 10 1 Drop size (mm) 0 1 2 3 4 5 6 7 Number of drops / m 3 / mm  = 5

31. Heavier rain D o Increases: N w  D o 2 If: N w  D o 2 More, larger drops as rain increases Similar to the NEXRAD default of Z  R 1.3 Convective/tropical rain? 10 4 10 3 10 2 10 1 Drop size (mm) 0 1 2 3 4 5 6 7 Number of drops / m 3 / mm  = 5

32. R from Z and Z DR Z DR is independent of N w, so gives us D o Fixed Z DR normalized gamma  D o const. For fixed Z DR, Z and R scale with N w For each Z DR calculate Z for R=1mm/hr dBZ R=1 = f (Z DR ) Use Andsager (‘99) or Goddard(’84) shapes Hence, dBR = dBZ OBS – f (Z DR )

33. Example: dBR = dBZ obs – f(Z DR ) 1mm/hr Need Z DR to 0.1dB @ 3mm/hr to 25% Observed Z DR =0.65dB For this Z DR : R of 1 mm/hr has 26.4dBZ Observed 36.4dBZ, so R=10dBR or 10mm/hr Now use to plot log R – dBZ space to calculate a and b dBZ obs f(Z dr)

34. Case Study 9 Oct 2000 Convective area Stratiform area

35. Convective case Data from a square side 4km. N w less than 8000 m -3 mm -1. N w seems to increase as R increases. Expect b < 1.5 Accuracy of observations Z  0.7dB Z DR  0.2dB

36. Convective case Convert Z and ZDR to log R – dBZ space ‘SD - line’ Slope  log Z /  log R Passing dBZ & log R a from intercept b from slope Error in R ± std For given Z, R changes 3dB which is factor of 2: but SD fit is to within 25% This data gives a=340, b=1.37 Z=340R 1.37 25% spread

37. Stratiform case Data from square side 4km. N w reduces as D o increases Expect b larger than 1.5

38. Stratiform case Convert Z, ZDR to logR – dBZ space Individual Z-R spread gives R spread 5dB. S-D line: given Z, R changes 1dB, 25% This data gives a=300 & b=1.58 Z=300R 1.58 25% spread

39. Summary Different Z-R from domain averaged Z and ZDR. Individual Z- ZDR rainfall has big spread. Domain average spread in R is 1dB. The rain rate calculated from the 2 cases is quite different for rainrates >5mm/hr

40. Rainfall maps a and b are calculated over small areas and these then used to calculate R form Z=aR b

41. Zphi method